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Math Help - 3^(x-1) + 25^(3x/2) = 15628

  1. #1
    Member aldrincabrera's Avatar
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    Red face 3^(x-1) + 25^(3x/2) = 15628

    Good day...need ur help with this.. By trial and error, it is obvious that x=2. But how should we do this without using trial and error? That is, by any step by step method. If any. thanks
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    Forum Admin topsquark's Avatar
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    Re: 3^(x-1) + 25^(3x/2) = 15628

    Quote Originally Posted by aldrincabrera View Post
    Good day...need ur help with this.. By trial and error, it is obvious that x=2. But how should we do this without using trial and error? That is, by any step by step method. If any. thanks
    Unless you have a typo and the RHS is supposed to be 15625 then x = 2 is not a solution....it's just very very close to 2. As far as I am aware there is no Algebraic method to solve this equation.

    -Dan
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    Re: 3^(x-1) + 25^(3x/2) = 15628

    Quote Originally Posted by topsquark View Post
    Unless you have a typo and the RHS is supposed to be 15625 then x = 2 is not a solution....it's just very very close to 2. As far as I am aware there is no Algebraic method to solve this equation.

    -Dan
    I am still struggling with this one, wish me good luck, but x = 2 is exact: 3 + 25^3 = 15628
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    Forum Admin topsquark's Avatar
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    Re: 3^(x-1) + 25^(3x/2) = 15628

    Quote Originally Posted by votan View Post
    I am still struggling with this one, wish me good luck, but x = 2 is exact: 3 + 25^3 = 15628
    (Ahem!) I forgot about the 3^(x - 1) term. Sorry!

    Thanks for the catch.

    -Dan
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    Member aldrincabrera's Avatar
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    Re: 3^(x-1) + 25^(3x/2) = 15628

    Hehehe, its okay.. i just dont know how to do this without trial and error
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    Member aldrincabrera's Avatar
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    Re: 3^(x-1) + 25^(3x/2) = 15628

    i still cant get this... please help
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    Re: 3^(x-1) + 25^(3x/2) = 15628

    Aldrincambrera :
    As Top squark mentioned above such kind of equations cannot be solved using algebraic methods...however:
    transform the given equation into the form 3^x +3(125)^x =46884 then analyse the 46884 into the form 3^2+3(125)^2 and the solution x=2 is obvious.........
    Have a good day.

    In memory of my student Stefanos who died today ............may god bless his soul...........................
    Minoas
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    Re: 3^(x-1) + 25^(3x/2) = 15628

    You've already been told that there is not a way known to solve this equation exactly other than trial and error. If there are any other solutions you'll need to get approximations for them using numerical methods.
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  9. #9
    WLX
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    Re: 3^(x-1) + 25^(3x/2) = 15628

    3^(x-1)+25^(3/2x)=15628
    3^(x-1)+(25^3/2)x=5^6 + 3
    3^(x-1)+5^3x =5^6 + 3


    x-1 =1 3x=6
    x =2 x=2
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